Question: Jessica is 3 times as old as Gabriela. Twelve years ago, Jessica was 5 times as old as Gabriela. How old is Gabriela now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Gabriela. Let Jessica's current age be $j$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $j = 3g$ Twelve years ago, Jessica was $j - 12$ years old, and Gabriela was $g - 12$ years old. The information in the second sentence can be expressed in the following equation: $j - 12 = 5(g - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 3g$ . Substituting this into our second equation, we get: $3g$ $-$ $12 = 5(g - 12)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $3 g - 12 = 5 g - 60$ Solving for $g$ , we get: $2 g = 48.$ $g = 24$.